Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	2^352585-18901	106139	Enzo Doria	05/2013
8002	26363^10614+10614^26363	106135	Hans Havermann	09/2020
8003	(2^352554-3)/193	106128	Lelio R Paula	12/2013
8004	2^352540+15015	106126	Lelio R Paula	01/2017
8005	25068^17119+17119^25068	106125	Hans Havermann	09/2020
8006	2^352524-3149	106121	Yves Minet	10/2014
8007	(7*10^106119-67)/3	106120	Robert Price	10/2021
8008	2^352486-1858781	106109	Enzo Doria	04/2016
8009	2^352444+12705	106097	Lelio R Paula	01/2017
8010	28561^5182+5182^28561	106090	Hans Havermann	10/2020
8011	(182*10^106083+43)/9	106085	Robert Price	02/2020
8012	(266*10^106066+1)/3	106068	Robert Price	04/2020
8013	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
8014	2^352228-18953	106032	Enzo Doria	05/2013
8015	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
8016	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
8017	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
8018	2^352107+1872533	105995	Enzo Doria	05/2016
8019	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
8020	2^352066-2591	105983	Yves Minet	07/2014
8021	2^352030+715	105972	Lelio R Paula	10/2011
8022	9*6^136176-5	105967	Lelio R Paula	11/2014
8023	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
8024	122^50789-50789^122	105965	Norman Luhn	09/2024
8025	28582^5097+5097^28582	105963	Hans Havermann	09/2020
8026	155^48377+2	105962	Lelio R Paula	08/2013
8027	(23*10^105944-119)/3	105945	Robert Price	07/2021
8028	2^351865+1869707	105922	Enzo Doria	05/2016
8029	24974^17427+17427^24974	105921	Hans Havermann	09/2020
8030	25163^16194+16194^25163	105920	Hans Havermann	09/2020
8031	2^351831+23	105912	Lelio R Paula	10/2011
8032	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
8033	9*2^351784-5	105899	Lelio R Paula	09/2014
8034	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
8035	(85*10^105881+203)/9	105882	Robert Price	09/2020
8036	2^351671-112387	105864	Enzo Doria	06/2014
8037	2^351669-109501	105863	Enzo Doria	04/2014
8038	2^351644+74731	105856	Enzo Doria	04/2016
8039	13^95025-42	105853	Lelio R Paula	12/2016
8040	2^351599+15015	105842	Lelio R Paula	01/2017
8041	19^82763+90	105834	Lelio R Paula	01/2017
8042	(205*10^105831-1)/3	105833	Robert Price	11/2021
8043	26050^11551+11551^26050	105832	Hans Havermann	09/2020
8044	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
8045	20^81329-51	105812	Lelio R Paula	01/2017
8046	(5*10^105811+211)/9	105811	Robert Price	02/2018
8047	2^351483+28425	105807	Lelio R Paula	01/2017
8048	25231^15610+15610^25231	105804	Hans Havermann	09/2020
8049	15^89960+86	105802	Lelio R Paula	02/2017
8050	2^351460-17289	105801	Enzo Doria	05/2013
8051	19^82735+22	105798	Lelio R Paula	01/2017
8052	2^351435-109077	105793	Enzo Doria	04/2014
8053	2^351393+1089	105780	Lelio R Paula	01/2017
8054	2^351364+72631	105772	Enzo Doria	04/2016
8055	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
8056	26818^8783+8783^26818	105761	Hans Havermann	09/2020
8059	2^351305+1872467	105754	Enzo Doria	05/2016
8058	3^221649+16	105754	Lelio R Paula	11/2016
8057	32511^1790+1790^32511	105754	Hans Havermann	09/2020
8060	8*3^221637-5	105749	Lelio R Paula	09/2014
8061	2^351279-2780449	105746	Enzo Doria	03/2016
8062	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
8063	15^89903-26	105735	Lelio R Paula	02/2017
8065	2^351213-73	105726	Lelio R Paula	10/2011
8064	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
8066	2^351192-4589	105720	Yves Minet	07/2011
8067	20^81250-33	105709	Lelio R Paula	12/2016
8068	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
8069	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
8070	2^351076-113159	105685	Enzo Doria	07/2014
8071	93^53688-2	105684	Lelio R Paula	09/2013
8072	2^351060-4559	105680	Yves Minet	07/2011
8073	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
8074	11^101473-750	105674	Enzo Doria	11/2012
8075	3*5^151181-8	105672	Lelio R Paula	11/2014
8076	15^89831-34	105650	Lelio R Paula	02/2017
8078	11^101448-360	105648	Enzo Doria	08/2012
8077	3*7^125011+4	105648	Lelio R Paula	11/2014
8079	2^350943-113269	105645	Enzo Doria	07/2014
8080	2*10^105636-91	105637	Robert Price	04/2020
8081	24231^22880+22880^24231	105634	Hans Havermann	09/2020
8082	35296^983+983^35296	105626	Hans Havermann	09/2020
8083	2^350868-19725	105622	Enzo Doria	06/2013
8084	2^350858-59291	105619	Enzo Doria	10/2015
8085	V(758484)/1516967/19720583	105618	Serge Batalov	07/2024
8086	2^350851+135	105617	Lelio R Paula	10/2011
8087	2^350841-741	105614	Lelio R Paula	01/2017
8088	3*10^105582+77	105583	Robert Price	09/2018
8089	24915^17284+17284^24915	105581	Hans Havermann	09/2020
8090	(5*10^105576-53)/3	105577	Robert Price	09/2020
8091	8*10^105571+3	105572	Robert Price	08/2015
8092	2^350674-78557	105564	Jorge Menendez	03/2018
8093	2*5^151026-3	105563	Lelio R Paula	11/2014
8094	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
8095	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
8096	3^221211+236	105545	Lelio R Paula	11/2016
8097	(32*10^105530-77)/9	105531	Robert Price	06/2018
8098	10^105515+33	105516	Lelio R Paula	11/2016
8099	24644^19125+19125^24644	105516	Hans Havermann	10/2020
8100	10^105515-41033	105515	Patrick De Geest	12/2016
8101	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
8102	2^350455-430567	105498	Harrison Mesh	06/2022
8103	17^85732-72	105489	Lelio R Paula	01/2017
8104	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
8105	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
8106	2^350356+24241	105468	Enzo Doria	10/2023
8107	25233^15118+15118^25233	105462	Hans Havermann	09/2020
8108	26261^10366+10366^26261	105454	Hans Havermann	09/2020
8109	2^350307-110329	105453	Enzo Doria	05/2014
8110	2^350253-20365	105437	Enzo Doria	06/2013
8111	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
8112	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
8113	4*10^105415-69	105416	Robert Price	01/2022
8114	21^79725-22	105414	Anonymous	09/2024
8115	(22*10^105407+179)/3	105408	Robert Price	02/2022
8116	2^350139-109009	105403	Enzo Doria	04/2014
8117	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
8118	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
8119	3*5^150763+4	105380	Lelio R Paula	11/2014
8120	12^97643+91	105375	Lelio R Paula	02/2017
8121	6*5^150744-7	105367	Lelio R Paula	11/2014
8122	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
8123	4*10^105364-39	105365	Robert Price	09/2020
8124	Phi(156135,-5#)	105361	Henri Lifchitz	12/2025
8126	2^349996-112169	105360	Enzo Doria	06/2014
8125	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
8127	(418*10^105343+23)/9	105345	Robert Price	02/2020
8128	25490^13563+13563^25490	105334	Hans Havermann	10/2020
8129	(5^504004)%F(504004)	105330	Henri Lifchitz	06/2025
8130	11^101142-1080	105329	Enzo Doria	12/2012
8131	(68*10^105320-41)/9	105321	Robert Price	10/2013
8132	24800^17649+17649^24800	105319	Hans Havermann	09/2020
8133	3^220712-9934	105307	Enzo Doria	05/2014
8134	7*10^105296+9	105297	Robert Price	09/2015
8135	89*10^105284-7	105286	Robert Price	04/2020
8136	2^349739+1873373	105282	Enzo Doria	06/2016
8137	7^124574+24	105278	Lelio R Paula	11/2016
8138	2^349708-20957	105273	Enzo Doria	06/2013
8139	34115^1218+1218^34115	105267	Hans Havermann	09/2020
8140	24029^24029-24020^24020	105265	Henri Lifchitz	09/2024
8141	2^349649-20469	105255	Enzo Doria	06/2013
8142	2^349607-20109	105243	Enzo Doria	06/2013
8143	(85*10^105242+473)/9	105243	Robert Price	01/2020
8144	2^349594-19085	105239	Enzo Doria	05/2013
8145	2^349530+1874479	105220	Enzo Doria	06/2016
8146	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
8147	(106*10^105199+17)/3	105201	Robert Price	04/2021
8148	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
8149	3^220464-112852	105189	Enzo Doria	07/2014
8150	2^349419-17349	105186	Enzo Doria	05/2013
8151	2^349400-2579	105180	Yves Minet	07/2014
8152	8*5^150471+3	105176	Lelio R Paula	11/2014
8153	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
8154	655^37342+37342^655	105165	Norbert Schneider	08/2018
8155	13^94403+94	105160	Lelio R Paula	12/2016
8156	349315*2^349315+3	105160	Anonymous	09/2025
8157	2^349301-112309	105151	Enzo Doria	06/2014
8158	30291^2960+2960^30291	105149	Hans Havermann	09/2020
8159	Phi(269776,7)	105144	Henri Lifchitz	02/2026
8160	27350^6981+6981^27350	105132	Hans Havermann	09/2020
8162	9*2^349220+5	105127	Lelio R Paula	09/2014
8161	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
8163	7*3^220317+8	105119	Lelio R Paula	09/2014
8164	7^124386+88	105119	Lelio R Paula	11/2016
8165	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
8166	2^349171-19657	105111	Enzo Doria	06/2013
8167	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
8168	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
8169	(2^349111-5)/3	105093	Lelio R Paula	12/2013
8170	675^37142+37142^675	105087	Norbert Schneider	08/2018
8171	2^348981-2797573	105054	Enzo Doria	04/2016
8172	(445^39667+1)/446	105050	Jinyuan Wang	05/2024
8173	2^348869-6555	105021	Lelio R Paula	01/2017
8174	10^105003-17319	105003	Alfred Reich	08/2024
8175	5^150217+78	104998	Lelio R Paula	11/2016
8176	(88*10^104989-1)/3	104991	Robert Price	04/2020
8177	(28*10^104972+149)/3	104973	Robert Price	12/2019
8178	24927^16262+16262^24927	104972	Hans Havermann	10/2020
8179	2^348703-113005	104971	Enzo Doria	06/2014
8180	(191*10^104956-17)/3	104958	Robert Price	11/2021
8181	2^348612-809	104943	Yves Minet	05/2013
8182	(73*10^104942-1)/9	104943	Robert Price	01/2015
8183	(29^71761-5^71761)/24	104942	Robert Price	03/2026
8184	2^348583-350407	104934	Enzo Doria	06/2015
8185	2^348531-949	104919	Yves Minet	05/2012
8186	20^80636-59	104910	Lelio R Paula	12/2016
8187	8*10^104893-13	104894	Robert Price	08/2019
8189	2^348437+35	104890	Lelio R Paula	09/2011
8188	25208^14487+14487^25208	104890	Hans Havermann	09/2020
8190	2^348348+135	104864	Lelio R Paula	09/2011
8191	(29*10^104858+349)/9	104859	Robert Price	06/2021
8192	6*10^104852-31	104853	Robert Price	07/2020
8194	(2^348284+9)/25	104843	Lelio R Paula	12/2013
8193	75^55914-74	104843	Norbert Schneider	01/2015
8195	2^348268+255255	104840	Lelio R Paula	01/2017
8196	35540^891+891^35540	104839	Hans Havermann	09/2020
8197	5^149985-52	104836	Lelio R Paula	11/2016
8198	2^348224-20249	104826	Enzo Doria	06/2013
8199	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
8200	2^348212-20105	104823	Enzo Doria	06/2013
8201	24647^17898+17898^24647	104819	Hans Havermann	10/2020
8202	20^80562+19	104814	Lelio R Paula	12/2016
8203	2*10^104811-87	104812	Robert Price	04/2018
8204	2^348149-20053	104804	Enzo Doria	06/2013
8205	Phi(341301,3)	104792	Henri Lifchitz	12/2025
8206	2^348095-171	104788	Lelio R Paula	09/2011
8207	25383^13412+13412^25383	104769	Hans Havermann	09/2020
8208	2^348003-20377	104760	Enzo Doria	06/2013
8209	26^74036-27	104759	Anonymous	09/2024
8211	2^347994-741	104757	Lelio R Paula	12/2016
8210	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
8212	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
8213	25137^14702+14702^25137	104756	Hans Havermann	09/2020
8214	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
8215	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
8216	2^347910-109937	104732	Enzo Doria	04/2014
8217	(88*10^104709-637)/9	104710	Robert Price	11/2020
8218	(13*10^104702+71)/3	104703	Robert Price	06/2021
8219	5^149794+28	104702	Lelio R Paula	11/2016
8220	105^51800-2	104698	Lelio R Paula	10/2017
8221	(16^86939+3^86939)/19	104684	Robert Price	06/2013
8222	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
8223	2^347731-18609	104678	Enzo Doria	05/2013
8224	4*6^134519+7	104677	Lelio R Paula	11/2014
8225	(34*10^104672-259)/9	104673	Robert Price	12/2021
8226	25321^13588+13588^25321	104656	Hans Havermann	09/2020
8227	2^347625+5367	104646	Riley Fisher	04/2023
8228	2^347612-18545	104642	Enzo Doria	05/2013
8229	6^134465+95	104635	Lelio R Paula	11/2016
8231	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
8230	(166*10^104633-7)/3	104635	Robert Price	11/2020
8232	V(750972)/15019441	104621	Serge Batalov	07/2024
8233	2^347517-17301	104614	Enzo Doria	05/2013
8234	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
8235	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
8236	3^219222-310	104596	Lelio R Paula	11/2016
8237	25993^10554+10554^25993	104581	Hans Havermann	09/2020
8238	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
8239	2^347372-17853	104570	Enzo Doria	05/2013
8240	2^347314+99	104552	Lelio R Paula	09/2011
8241	2^347300-22233	104548	Enzo Doria	06/2013
8242	2^347287-19845	104544	Enzo Doria	06/2013
8243	2^347258-231191	104536	Harrison Mesh	06/2022
8244	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
8245	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
8246	7*2^347239-3	104531	Lelio R Paula	09/2014
8247	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
8248	5*3^219047+8	104513	Lelio R Paula	09/2014
8249	2^347148-109073	104502	Enzo Doria	04/2014
8250	2^347129-20145	104497	Enzo Doria	06/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302825 PRPs in the top)